document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007160>Question 1007160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+1%2F%282x%5E3-9%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+1%2F%282x%5E3-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623148 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f^-1(x) is the inverse function of f(x).\r<BR>\n" );
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document.write( "let y = f(x).\r<BR>\n" );
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document.write( "you get y = 1/(2x^3-9)\r<BR>\n" );
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document.write( "replace y with x and x with y and you get:\r<BR>\n" );
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document.write( "x = 1/(2y^3-9)\r<BR>\n" );
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document.write( "that's your inverse equation.\r<BR>\n" );
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document.write( "what's left is to solve for y if you can.\r<BR>\n" );
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document.write( "if not, go with it the way it is.\r<BR>\n" );
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document.write( "this one can be solved for y.\r<BR>\n" );
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document.write( "start with x = 1/(2y^3-9)\r<BR>\n" );
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document.write( "multiply both sides of the equation by (2y^3-9) and divide both sides of the equation by x.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "2y^3 - 9 = 1/x\r<BR>\n" );
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document.write( "add 9 to both sides of the equation to get:\r<BR>\n" );
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document.write( "2y^3 = 1/x + 9\r<BR>\n" );
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document.write( "since 1/x + 9 is the same as (1+9x)/x, the equation becomes:\r<BR>\n" );
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document.write( "2y^3 = (1+9x)/x\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
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document.write( "y^3 = (1+9x)/(2x)\r<BR>\n" );
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document.write( "take the third root of both sides of the equation to get:\r<BR>\n" );
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document.write( "y = ((1+9x)/(2x))^(1/3)\r<BR>\n" );
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document.write( "that's your inverse equation after you have solved for y.\r<BR>\n" );
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document.write( "the grpah of the equation plus its inverse is shown below.\r<BR>\n" );
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document.write( "the graphs also includes the line y = x which they need to be a reflection of in order to be inverse equations.\r<BR>\n" );
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document.write( "the graph also includes lines y = -x + 5 and y = -x - 5 thst shows that the points are reflections about the line y = x.\r<BR>\n" );
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document.write( "that's because (x,y) on the original equation equals (y,x) on the inverse equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/120103.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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